A Unified Theory of Computational Waste: The Ontometric Foundation of Relational Calculus

Artificial intelligence and physical simulation are suffocating under a self-imposed computational burden. A Unified Theory of Computational Waste identifies the root cause of this inefficiency not as a hardware limitation, but as a fundamental ontological error in how we mathematically represent reality: the imposition of absolute, external measurement scales onto self-contained systems.

This paper introduces Ontometric Relational Calculus, a rigorous mathematical and architectural framework that resolves this structural mismatch. We derive and empirically validate the $O=D^2$ law, proving that unnecessary computational overhead scales quadratically with the distortion between imported units (e.g., Kelvin, meters) and a system's intrinsic dynamics. This "dimensional tax" inflates the condition number of optimization landscapes and leads to massive energy waste in modern deep learning. Worse, it relies on mathematical infinities that blind conventional models to critical phase transitions.

The solution is to let the system act as its own measure. By architecting models around bounded, dimensionless ratios anchored to a system’s theoretical physical limits (its "North Star"), we collapse optimization overhead to a constant. Through empirical validation across six machine learning domains and classical physics simulations, this framework demonstrates:

• The collapse of optimization overhead and the mathematical eradication of technical debt.

• Scale invariance by construction, making predictions immune to arbitrary changes in unit systems.

• Zero-shot phase transition extrapolation, allowing models to cleanly cross critical boundaries where conventional AI catastrophically fails.

Bridging Landauer’s thermodynamics of information with Kolmogorov’s algorithmic complexity, this manifesto provides the theoretical proofs, the architectural guidelines, and the reproducible code to eliminate structural computational waste. It is a definitive blueprint for mathematically stable, capital-efficient algorithm design and the realization of true Green AI.